The Northern Irishman, who won his second successive Clydesdale Bank Premier League title this season and took the Hoops to the last 16 of the Champions League, is one of the favourites to take over from David Moyes at Goodison.
However, Auld, who played in the Celtic side which became the first British team to win the European Cup when they beat Inter Milan 2-1 in Lisbon in 1967, said: "I think Neil should be here next season. I think he has done a good job but I still think he has a lot to learn and I will tell you this much, it doesn't matter which club he goes to, it won't be the same as this one."
He added: "What he has to do is look into himself and say 'are any of these jobs better than the one I have?' I don't know what he thinks but I know one thing, any of the jobs which are up at this particular moment, they couldn't touch Celtic.
"It doesn't matter which jobs he gets offered, even the Everton job doesn't touch this one."
Auld, at Celtic Park for the launch of the book 'Celtic; The Awakening', believes there is plenty of room for improvement at Parkhead.
The former Hibernian and Partick Thistle manager referred back to the ethos of his two managers at Celtic Park during his two spells at the club which spanned the 1950s, 60s and 70s, Jimmy McGrory and Jock Stein, as he insisted that "three quality players" are required for next season.
"Neil Lennon is just a young boy and has a lot to learn," he said. "He has done extremely well. But I am disappointed because we have lost 35 points in the league this year. We had a pool of players that should have run away with the league but didn't.
"We are 13 points clear but the teams who beat us...that was disappointing. I honestly believe that Neil has to bring in three quality players to bring on the young players.
"Whether he is allowed to bring in another couple of players I couldn't tell you, but everybody in the stands will tell you we need another two or three quality players."
- Sports & Recreation
- Neil Lennon
- David Moyes
- Clydesdale Bank Premier League
- Celtic Park